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How does the electric potential due to a dipole vary on the dipole axis as a function of $r$ – distance of the field point from the mid–point of the dipole, at large distances?

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Important Questions on Electrostatic Potential and Capacitance

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A total charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure below. The electric potential at the point $O$ lying at a distance $\frac{L}{2}$ from the end $A$ is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Four point charges

- Q, - q, 2 q

and

2 Q

are placed, one at each corner of the square. The relation between

Q

and

q

for which the potential at the centre of the square is zero is

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A mass of

1 kg

carrying a charge of

2 C

is accelerated through a potential of

1 V

. The velocity acquired by it is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

When an

α

-particle of mass

m

moving with a undefined velocity bombards on a heavy nucleus of charge

Ze

, its distance of the closest approach from the nucleus depends on

m

as:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A certain p-n junction having a depletion region of width

20 μm,

was found to have a breakdown voltage of

100 V

. If the width of the depletion region is reduced to

1 μm

during its production, then it can be used as a zener diode for voltage regulation of:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Four capacitors with capacitances $C_{1} = 1 μF, C_{2} = 1.5 μF$ , $C_{3} = 2.5 μF$ and $C_{4} = 0.5 μF$ are connected as shown and are connected to a $30$ volt source. The potential difference between points $a$ and $b$ is:

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EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A hot filament liberates an electron with zero initial velocity. The anode potential is

1200 V

. The speed of the electron when it strikes the anode is

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

An electric field

\vec{E} = (25 \hat{i} + 30 \hat{j}) N C^{- 1}

exists in a region of space. If the potential at the origin is taken to be zero then the potential at

x = 2 m

y = 2 m

is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Two tiny spheres carrying charges

1.8 μ C

and

2.8 μ C

are located at

40 c m

apart. The potential at the mid-point of the line joining the two charges is

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Ten charges are placed on the circumference of a circle of radius

R

with constant angular separation between successive charges. Alternate charges

1, 3, 5, 7, 9

have charge

(+ q)

each, while

2, 4, 6, 8, 10

have charge

(- q)

each. The potential V and the electric field E at the centre of the circle are respectively : (Take

V = 0

at infinity)

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Four equal point charges

Q

each are placed in the

x y

plane at

(0, 2), (4, 2), (4, - 2)

and

(0, - 2)

. The work required to put a fifth charge

Q

at the origin of the coordinate system will be:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A charge

Q

is distributed over three concentric spherical shells of radii

a, b, c (a < b < c)

such that their surface charge densities are equal to one another.

The total potential at a point at distance

r

from their common centre, where

r < a,

would be:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Twenty seven drops of same size are charged at

220 V

each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

If potential(in

volts

) in a region is expressed as

V (x, y, z) = 6 x y - y + 2 y z

, the electric field(in

N C^{- 1}

) at point

(1, 1, 0)

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Two equal charges of magnitude

Q

each are placed at a distance

d

apart. Their electrostatic energy is

E . A .

third charge

- \frac{Q}{2}

is brought midway between these two charges. The electrostatic energy of the system is now?

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

The variation of electrostatic potential with radial distance

r

from the centre of a positively charged metallic thin shell of radius

R

is given by the graph

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

An electron with an initial speed of

4 .0 \times 10^{6} m s^{- 1}

is brought to rest by an electric field. The mass and charge of an electron are

9 \times 10^{- 31} kg

and

1.6 \times 10^{- 19} C

, respectively. Identify the correct statement.

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electric Potential

Consider a cube of uniform charge density,

ρ

. The ratio of the electrostatic potential at the center of the cube to that at one of the corners of the cube is,

How does the electric potential due to a dipole vary on the dipole axis as a function of r– distance of the field point from the mid–point of the dipole, at large distances?

Important Questions on Electrostatic Potential and Capacitance

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How does the electric potential due to a dipole vary on the dipole axis as a function of $r$ – distance of the field point from the mid–point of the dipole, at large distances?